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| Title:
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On the Duality Principle by Casazza, Kutyniok, and Lammers |
| Type:
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Journal articleJournal article |
| Participant(s):
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Technical University of Denmark
Email:
Forfatter:
Kim, Hong Oh
KAIST, Department of Mathematical Sciences
Forfatter:
Kim, Rae Young
Yeungnam University, Department of Mathematics
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| Abstract:
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The R-dual sequences of a frame {f i } i∈I , introduced by Casazza, Kutyniok and Lammers in (J. Fourier Anal. Appl. 10(4):383–408, 2004), provide a powerful tool in the analysis of duality relations in general frame theory. In this paper we derive conditions for a sequence {ω j } j∈I to be an R-dual of a given frame {f i } i∈I . In particular we show that the R-duals {ω j } j∈I can be characterized in terms of frame properties of an associated sequence {n i } i∈I . We also derive the duality results obtained for tight Gabor frames in (Casazza et al. in J. Fourier Anal. Appl. 10(4):383–408, 2004) as a special case of a general statement for R-duals of frames in Hilbert spaces. Finally we consider a relaxation of the R-dual setup of independent interest. Several examples illustrate the results. |
| Published:
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in journal: Journal of Fourier Analysis and Applications (ISSN: 10695869) (DOI: http://dx.doi.org/10.1007/s00041-010-9151-4), vol: 17, issue: 4, pages: 640-655, 2011 |
| DOI:
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